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There have been many attempts to solve the P versus NP problem. However, with a new proof method, P not equal NP can be proved. A time limit is set for an arbitrary Turing machine and an input word is rejected on a timeout. The time limit…
Reconciling gene trees with a species tree is a fundamental problem to understand the evolution of gene families. Many existing approaches reconcile each gene tree independently. However, it is well-known that the evolution of gene families…
Rank minimization has attracted a lot of attention due to its robustness in data recovery. To overcome the computational difficulty, rank is often replaced with nuclear norm. For several rank minimization problems, such a replacement has…
Existing definitions of the relativizations of \NCOne, \L\ and \NL\ do not preserve the inclusions $\NCOne \subseteq \L$, $\NL\subseteq \ACOne$. We start by giving the first definitions that preserve them. Here for \L\ and \NL\ we define…
The Rabin tree theorem yields an algorithm to solve the satisfiability problem for monadic second-order logic over infinite trees. Here we solve the probabilistic variant of this problem. Namely, we show how to compute the probability that…
Convolutional Neural Networks (CNNs) excel in many visual tasks but remain susceptible to adversarial attacks-imperceptible perturbations that degrade performance. Prior research reveals that brain-inspired regularizers, derived from neural…
Finding roots of equations is at the heart of most computational science. A well-known and widely used iterative algorithm is the Newton's method. However, its convergence depends heavily on the initial guess, with poor choices often…
We show that Cutting Planes (CP) proofs are hard to find: Given an unsatisfiable formula $F$, 1) It is NP-hard to find a CP refutation of $F$ in time polynomial in the length of the shortest such refutation; and 2)unless Gap-Hitting-Set…
We study decision rule approximations for generic multi-stage robust linear optimization problems. We consider linear decision rules for the case when the objective coefficients, the recourse matrices, and the right-hand sides are…
Reinforcement learning (RL) problems are fundamental in online decision-making and have been instrumental in finding an optimal policy for Markov decision processes (MDPs). Function approximations are usually deployed to handle large or…
Training language models to solve complex mathematical problems benefits from curriculum learning progressively training on simpler subproblems. However, existing decomposition methods are often heuristic, offering no guarantees that…
Many satisfiability modulo theories solvers implement a variant of the DPLL(T ) framework which separates theory-specific reasoning from reasoning on the propositional abstraction of the formula. Such solvers conclude that a formula is…
Learned inverse problem solvers exhibit remarkable performance in applications like image reconstruction tasks. These data-driven reconstruction methods often follow a two-step scheme. First, one trains the often neural network-based…
Removal of noise from an image is an extensively studied problem in image processing. Indeed, the recent advent of sophisticated and highly effective denoising algorithms lead some to believe that existing methods are touching the ceiling…
The subject logic in computer science should entail proof theoretic applications. So the question arises whether open problems in computational complexity can be solved by advanced proof theoretic techniques. In particular, consider the…
Phylogenetic trees are leaf-labelled trees used to model the evolution of species. Here we explore the practical impact of kernelization (i.e. data reduction) on the NP-hard problem of computing the TBR distance between two unrooted binary…
We address the optimization problem in a data-driven variational reconstruction framework, where the regularizer is parameterized by an input-convex neural network (ICNN). While gradient-based methods are commonly used to solve such…
Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in…
Regularization techniques such as $\mathcal{L}_1$ and $\mathcal{L}_2$ regularizers are effective in sparsifying neural networks (NNs). However, to remove a certain neuron or channel in NNs, all weight elements related to that neuron or…
We introduce the refined assortment optimization problem where a firm may decide to make some of its products harder to get instead of making them unavailable as in the traditional assortment optimization problem. Airlines, for example,…